Endohedral complexes of fullerenes and noble-gas atoms were originally prepared by a mass spectrometric method involving high-energy collisions of fullerene ions and noble-gas targets and, following that, by a high-pressure, high-temperature method involving neutral fullerenes and a noble gas as reactants. The latter method has made available sufficient quantities of the endohedral complexes of C-60 and C-70 with the various noble gases (He, Ne, Ar, and Kr) that the tandem mass spectrometric method can be used to test the possibility of preparing a new class of endohedral complexes that contain two noble-gas atoms. These new capture complexes do indeed form upon activation of the radical cation of the noble-gas endohedral complex by high-energy collisions with helium atoms. These complexes then decompose to give equivalent parallel losses of C-2 units accompanied by expulsion of none, one, or both of the captured noble-gas atoms. The capture event causes the gain in excess of 34 eV of additional internal energy, but the capture complexes survive on the time scale (similar to 50 mu s) for the transit through the tandem mass spectrometer. Their survival, along with their fragmentation characteristics, is consistent with formation of an endohedral complex containing both noble-gas atoms although the fullerene cage may now be distorted especially when the fullerene is C-60. By analogy with the properties of empty fullerene and endohedral metallofullerene complexes, end points exist for the equivalent number of C-2 units that can be expelled to give a closed-structure product that contains either one or two noble-gas atoms. These end points correlate directly with the sizes of the fullerene and the noble-gas atom(s), giving support to our conclusion that endohedral complexes containing two noble gases can be prepared.